We have
numerically and experimentally investigated the flow modes of Taylor-Couette
system consisting of coaxial two cylinders with vertical axes. The inner
cylinder rotates and the outer cylinder and the bottom end of the cylinders
remain stationary. The upper top boundary is the free surface of the working
liquid between the inner and outer cylinders and it contacts with the air.
While this flow appears in fluid machinery and chemical reactors and includes
industrial interests, it also contains problems of fluid mechanics, which is
about the behavior of the free surface in the rotating field. In this paper, we
concretely show the developments of the one cell mode flow and the three cell
mode flow at a small aspect ratio. We also represent the bifurcation diagram of
the flow at the moderate aspect ratio about 5.5. In the numerical simulation,
the flow is rest in the initial state, and the inner cylinder is linearly or
suddenly accelerated to attain a flow with a prescribed Reynolds number. When
the acceleration of the inner cylinder is high, an imperfect bifurcation occurs
and the flows of the secondary modes emerge. At high Reynolds numbers, the flow
first has many vortices and then some of the vortices collapse and the final
stable flow arises. The loci of the normal five cell mode, the anomalous six
cell mode and the secondary seven cell mode are determined.

Nakamura, I., Toya, Y., Yamashita, S. and Ueki, Y. (1990) An Experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio (Bifurcation of Flows in a Symmetric System). JSME International Journal. Series II, 33, 685-691.

Nakamura, I., Toya, Y., Yamashita, S. and Ueki, S. (1989) An experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio (Instability of Taylor Vortex Flows). JSME International Journal. Series II, 23, 388-394.

Toya, Y., Nakamura, I., Yamashita, S. and Ueki, S. (1994) An Experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio: Bifuration of Flows in an Asymmetric system. Acta Mechanica, 102, 137-148.http://dx.doi.org/10.1007/BF01178523